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a doll sold for $203 in 1976 and was sold again in 1986 for $453. assume that the growth in the value V of the collectors item was exponential. A) find the alue of k of the exponential growth rate. assume V(sub) 0=203 k=?

1986 - 1976 = 10 years of growth in Value.

453 / 203 =2.2315271 - total growth in value over 10 years.

(2.2315271)^(1/10) ==1.0835781 - 1  x  100 =8.35781% - annual exponential (compounding) growth over 10 years. If you wish to convert it to continuous growth, just take the natural log(ln) of 1.0835781 =8.02686% .

You didn't include th equation,

   but set h= to 0  ( this is the height when the ball hits the grouand)  then solve the equation for t using the quadratic formula.

Wow....cool!  That is good to know !  ......maybe not.

We  have this system

5H + 4I  =  62

8H  + 12I  =  144        where H is the cost  for one hosta and I is the  price of an  ivy pot

Multiply the top equation through by  -3   and we  get that

-15H   -12 I   =  -186            and write the second equation

8H   +  12 I   =    144 

Add  the equations and we  get that

-7H  =  -42     divide both sides  by  -7

H  =6  (dollars)  = cost for  one hosta...

2. The lengths of two sides of an isosceles triangle are 10 and 12 centimeters. Find all possible values of the area of this triangle. 

Either  the remaining side is  10  or it is 12

If it is 10

Semi-perimeter, S  =   (10 + 10 + 12)  / 2  =   16

Area  = sqrt  [ S ( S - A)  (S - B)  (S - C)  ]    where A,B,C  are the side lengths

Area =   sqrt [  16  ( 16 - 10)  (16-10)(16-12)  ]  =   sqrt [ 16 * 6 * 6 * 4 ]  =  sqrt [ 16 * 36 *4 ] = 4*6*2  = 48

If it is 12

Semi-perimeter  =  (10 + 12 + 12)  / 2 =  17

Area  = sqrt [  17  (17 -12) (17-12) ( 17 -10)  ]  =  sqrt  [  17 * 5 *5 * 7  ]  =  sqrt [ 119 * 25 ]  =  5sqrt (119)

We  have

[  ( -6 +  (2/3)(15 - -6)  ,   19 +  (2/3) (-5 - 19)  ]   =

[ -6 + (2/3) (21)  ,  19 + (2/3) (-24)  ]   =

[  -6 + 14  ,  19  -16  ]  =

( 8 , 3)

n = 42

Note  that  1/5  gal  fills  2/3 of the  bin

So....we can use a proportion  to  find  the amount we  need

1/5 gal            ??? gal

______  =    ________       cross-multiply

2/3 bin             1 bin

1 * (1/5)  =   (???) *  (2/3)

1/5  = ( ???)  * (2/3)        multiply  both sides  by  (3/2).....this will cancel the fraction on the right  and we have that

(1/5) (3/2)  = (???)

(3 / 10 )  gallons  = (???)   .....the amount  to  fill the whole tank

a)  you are  correct....she started  with $200  and she ended up with $60

b) again,  correct....David starts with about $270

c)  again, good job .....Diana;s acct  never changes

d)  hard  to tell exactly on this graph  but

Denise  =$60

David  = $ 270

Diana  =  $ 200

To find the  final  amount.....got to the final point on each graph.....read staraight  across to  find that amt  on   the  "Amount"  axis

Here's one  method  to  find P

Construct  a  circle   with a center at  (0,0)  with a radius  of   sqrt (10)

The equation of this circle  is  x^2  +  y ^2 =  10     (1)

Similarly.....at B  construct  a circle  with a radius  of  3sqrt (2)   =   sqrt (18)

The equation of this circle  is  x^2 + ( y-4)^2  = 18     (2)

Subtracting (1)  from (2)   we  have that

( y - 4)^2  - y^2  =  8   simplify

y^2  - 8y  +  16  - y^2   =   8

-8y   +  16  =  8

-8y =  -8      →    y = 1

And to  find  x  we have that

x^2  + (1)^2    = 10

x^2   +  1   =10

x^2  = 9       take the  positive  root

x   =  3

So  P  =  ( 3,1)

Using the  distance  formula

CP  = sqrt  [( 5-3)^2  +  ( 1 - 0)^2  ]  =    sqrt [ 2^2  + 1^2 ]  =     sqrt (5)

what is 1\2 times 1\3   

    1                            2                      2        1  

   ––  is the same as  ––.       Half of  ––  is  ––.   

    3                            6                      6         6  

I really need the answers!

a) Danise's account but i dont know why. do you have an explanation cphill?

b) Dvids account but how?

c) Diana 's account but how?

d) i am having trouble

Triangle ABC has vertices A(0, 5), B(12, 0), C(0, 0) in the coordinate plane. The image when triangle ABC is rotated clockwise about the origin is triangle A'B'C' with vertex A'(3,4). What fraction of the area of triangle A'B'C' is below the x-axis? Express. your answer as a common fraction.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

9/14 of the whole area of triangle A'B'C' went below the x-axis. 

a)   Which  graph  has the line  that falls from left to right????

b)  Which graph has the line that rises from left to right  ???

c)  Which gra[h neither  rises  nor  falls from left to  right  ???

d) Look at  the final point on the  right hand end of each graph.......then ......go over  to the "Amount"  axis and  read  that value  [ hint.....in Diana's account....she looks like she has about  $200  at the end  ]

Let me  know if you have trouble......

The numerator is defined for all real numbers

We  need  to  have  complex roots  for the  polynomial in the  denominator

This will happen when  the discriminant is  <  0    ....so....

6^2  - 4c   <   0

36  - 4c  <  0

36 <  4c

9  <  c    means the  same thing as   c <  9

So....when  c  = 10, this rational function will have a domain of all reals

See  the graph here to  confirm this  : https://www.desmos.com/calculator/mkpngao0r3

EC  = (1/3) 50 =   50/3

ED =  (2/3) 50   =  100/3

And triangle  DFE  ≈  triangle  BFA

So DF / BF  =   (100/3) / 50  =  2/3

And triangle DBC ≈  triangle  FBG 

But  BF / BD  =  BF  / (BF + DF)  =  3 / (3 + 2)  =   3/5

Therefore

FG/ DC =  FB/ BD

FG  / 50  =  3/5

FG  =  50  (3/5)  =  30

Geometric approach: The equation |z - 3 - 5i| = 2 represents the line z - 3 - 5i = r*e^(i theta).  The equation |z - 6 - 6i| = 4 represents the line z - 6 - 6i = s*e^(j*theta).  The lines intersect in only one point, so there is only one solution z.

By the parallelogram law, the only possible value of d is 7 - 4i.

Can you please put the question in the question box.

You can put something similar in the heading as well if you want but ALL the question needs to be in the question box.

∠FEH = tan^-1(DE / AD)     Incorrect! 

∠FEH = tan^-1(AD / DE)     Correct! 

Thanks Chris. :)

A 4-pack of ice cream sandwiches costs $3.39. What is the unit price, rounded to the nearest cent?
 

AB = BC = CD = 50          

DE = 2/3 * 50           DE = 33.334

∠FEH = tan^-1(DE / AD)

Using the law of sines we can calculate DF and EF.     (DF = 28.284, EF = 24.037)

When we have all 3 sides of ΔDFE, we can calculate the triangle's area.   [DFE] = 333.334 u²

Height  FH = 2[DFE] / DE    ==>    FH = 20

BG = FG = BC - FH                     FG = 30 units